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CT-MQC – a coupled-trajectory mixed quantum/classical method including nonadiabatic quantum coherence effects

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Abstract

Upon photoexcitation by a short light pulse, molecules can reach regions of the configuration space characterized by strong nonadiabaticity, where the motion of the nuclei is strongly coupled to the motion of the electrons. The subtle interplay between the nuclear and electronic degrees of freedom in such situations is rather challenging to capture by state-of-the-art nonadiabatic dynamics approaches, limiting therefore their predictive power. The Exact Factorization of the molecular wavefunction, though, offers new perspectives in the solution of this longstanding issue. Here, we investigate the performance of a mixed quantum/classical (MQC) limit of this theory, named Coupled Trajectory-MQC, which was shown to reproduce the excited-state dynamics of small systems accurately. The method is applied to the study of the photoinduced ring opening of oxirane and the results are compared with two other nonadiabatic approaches based on different Ansätze for the molecular wavefunction, namely Ehrenfest dynamics and Ab Initio Multiple Spawning (AIMS). All simulations were performed using linear-response time-dependent density functional theory. We show that the CT-MQC method can capture the (de)coherence effects resulting from the dynamics through conical intersections, in good agreement with the results obtained with AIMS and in contrast with ensemble Ehrenfest dynamics.

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References

  1. R. Kapral, G. Ciccotti, J. Chem. Phys. 110, 8916 (1999)

    Article  ADS  Google Scholar 

  2. F. Agostini, S. Caprara, G. Ciccotti, Europhys. Lett. 78, 30001 (2007)

    Article  ADS  Google Scholar 

  3. T. Yonehara, K. Hanasaki, K. Takatsuka, Chem. Rev. 112, 499 (2012)

    Article  Google Scholar 

  4. J.C. Tully, J. Chem. Phys. 137, 22A301 (2012)

    Article  Google Scholar 

  5. M. Vacher, M.J. Bearpark, M.A. Robb, J.P. Malhado, Phys. Rev. Lett. 118, 083001 (2017)

    Article  ADS  Google Scholar 

  6. M. Born, R.J. Oppenheimer, Ann. Phys. 389, 457 (1927)

    Article  Google Scholar 

  7. C. Xie, C.L. Malbon, D.R. Yarkony, D. Xie, H. Guo, J. Am. Chem. Soc. 140, 1986 (2018)

    Article  Google Scholar 

  8. A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, Phys. Rev. X 7, 031035 (2017)

    Google Scholar 

  9. A. Schild, F. Agostini, E.K.U. Gross, J. Phys. Chem. A 120, 3316 (2016)

    Article  Google Scholar 

  10. A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, J. Chem. Phys. 143, 074106 (2015)

    Article  ADS  Google Scholar 

  11. L. Wang, A. Akimov, O.V. Prezhdo, J. Phys. Chem. Lett. 7, 2100 (2016)

    Article  Google Scholar 

  12. B.F.E. Curchod, U. Rothlisberger, I. Tavernelli, ChemPhysChem 14, 1314 (2013)

    Article  Google Scholar 

  13. I. Tavernelli, Acc. Chem. Res. 48, 792 (2015)

    Article  Google Scholar 

  14. J.E. Subotnik, A. Jain, B. Landry, A. Petit, W. Ouyang, N. Bellonzi, Ann. Rev. Phys. Chem. 67, 387 (2016)

    Article  ADS  Google Scholar 

  15. J.C. Tully, J. Chem. Phys. 93, 1061 (1990)

    Article  ADS  Google Scholar 

  16. J.C. Tully, Faraday Discuss. 110, 407 (1998)

    Article  ADS  Google Scholar 

  17. J.C. Tully, Faraday Discuss. 110, 407 (1998)

    Article  ADS  Google Scholar 

  18. F. Agostini, S.K. Min, A. Abedi, E.K.U. Gross, J. Chem. Theory Comput. 12, 2127 (2016)

    Article  Google Scholar 

  19. M. Ben-Nun, J. Quenneville, T.J. Martínez, J. Phys. Chem. A 104, 5161 (2000)

    Article  Google Scholar 

  20. E. Tapavicza, I. Tavernelli, U. Rothlisberger, Phys. Rev. Lett. 98, 023001 (2007)

    Article  ADS  Google Scholar 

  21. B.F.E. Curchod, T.J. Penfold, U. Rothlisberger, I. Tavernelli, Phys. Rev. A 84, 042507 (2011)

    Article  ADS  Google Scholar 

  22. A. Abedi, F. Agostini, E.K.U. Gross, Europhys. Lett. 106, 33001 (2014)

    Article  ADS  Google Scholar 

  23. F. Agostini, A. Abedi, E.K.U. Gross, J. Chem. Phys. 141, 214101 (2014)

    Article  ADS  Google Scholar 

  24. N.L. Doltsinis, D. Marx, Phys. Rev. Lett. 88, 166402 (2002)

    Article  ADS  Google Scholar 

  25. A.W. Jasper, S. Nangia, C. Zhu, D.G. Truhlar, Acc. Chem. Res. 39, 101 (2006)

    Article  Google Scholar 

  26. B.F.E. Curchod, I. Tavernelli, U. Rothlisberger, Phys. Chem. Chem. Phys. 13, 3231 (2011)

    Article  Google Scholar 

  27. P. Huo, D.F. Coker, J. Chem. Phys. 137, 22A535 (2012)

    Article  Google Scholar 

  28. R. Mitrić, J. Petersen, V. Bonačić-Koutecký, Phys. Rev. A 79, 053416 (2009)

    Article  ADS  Google Scholar 

  29. M. Richter, P. Marquetand, J. González-Vázquez, I. Sola, L. González, J. Chem. Theory Comput. 7, 1253 (2011)

    Article  Google Scholar 

  30. R. Kapral, Annu. Rev. Phys. Chem. 57, 129 (2006)

    Article  ADS  Google Scholar 

  31. E.R. Dunkel, S. Bonella, D.F. Coker, J. Chem. Phys. 129, 114106 (2008)

    Article  ADS  Google Scholar 

  32. T.J. Martínez, M. Ben-Nun, R.D. Levine, J. Phys. Chem. 100, 7884 (1996)

    Article  Google Scholar 

  33. T.J. Martínez, R.D. Levine, J. Chem. Soc. Faraday Trans. 93, 941 (1997)

    Article  Google Scholar 

  34. M. Ben-Nun, T.J. Martínez, J. Chem. Phys. 108, 7244 (1998)

    Article  ADS  Google Scholar 

  35. M.D. Hack, A.M. Wensmann, D.G. Truhlar, M. Ben-Nun, T.J. Martínez, J. Chem. Phys. 115, 1172 (2001)

    Article  ADS  Google Scholar 

  36. M. Ben-Nun, T.J. Martínez, Adv. Chem. Phys. 121, 439 (2002)

    Google Scholar 

  37. B.F.E. Curchod, C. Rauer, P. Marquetand, L. González, T. Martínez, J. Chem. Phys. 144, 101102 (2016)

    Article  ADS  Google Scholar 

  38. A.M. Virshup, C. Punwong, T.V. Pogorelov, B.A. Lindquist, C. Ko, T.J. Martínez, J. Phys. Chem. B 113, 3280 (2008)

    Article  Google Scholar 

  39. F.F. de Carvalho, M.E.F. Bouduban, B.F.E. Curchod, I. Tavernelli, Entropy 16, 62 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  40. A. Abedi, F. Agostini, Y. Suzuki, E.K.U. Gross, Phys. Rev. Lett. 110, 263001 (2013)

    Article  ADS  Google Scholar 

  41. F. Agostini, A. Abedi, Y. Suzuki, E.K.U. Gross, Mol. Phys. 111, 3625 (2013)

    Article  ADS  Google Scholar 

  42. F. Agostini, A. Abedi, Y. Suzuki, S.K. Min, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 142, 084303 (2015)

    Article  ADS  Google Scholar 

  43. A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010)

    Article  ADS  Google Scholar 

  44. A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 137, 22A530 (2012)

    Article  Google Scholar 

  45. S.K. Min, F. Agostini, E.K.U. Gross, Phys. Rev. Lett. 115, 073001 (2015)

    Article  ADS  Google Scholar 

  46. S.K. Min, F. Agostini, I. Tavernelli, E.K.U. Gross, J. Phys. Chem. Lett. 8, 3048 (2017)

    Article  Google Scholar 

  47. G. Granucci, M. Persico, J. Chem. Phys. 126, 134114 (2007)

    Article  ADS  Google Scholar 

  48. A.W. Jasper, S. Nangia, C. Zhu, D.G. Truhlar, Acc. Chem. Res. 39, 101 (2006)

    Article  Google Scholar 

  49. H.M. Jaeger, S. Fischer, O.V. Prezhdo, J. Chem. Phys. 137, 22A545 (2012)

    Article  Google Scholar 

  50. J.E. Subotnik, W. Ouyang, B.R. Landry, J. Chem. Phys. 139, 214107 (2013)

    Article  ADS  Google Scholar 

  51. X. Gao, W. Thiel, Phys. Rev. E 95, 013308 (2017)

    Article  ADS  Google Scholar 

  52. B.J. Schwartz, E.R. Bittner, O.V. Prezhdo, P.J. Rossky, J. Chem. Phys. 104, 5942 (1996)

    Article  ADS  Google Scholar 

  53. J.Y. Fang, S. Hammes-Schiffer, J. Phys. Chem. A 103, 9399 (1999)

    Article  Google Scholar 

  54. N. Shenvi, J.E. Subotnik, W. Yang, J. Chem. Phys. 134, 144102 (2011)

    Article  ADS  Google Scholar 

  55. N. Shenvi, J.E. Subotnik, W. Yang, J. Chem. Phys. 135, 024101 (2011)

    Article  ADS  Google Scholar 

  56. N. Shenvi, W. Yang, J. Chem. Phys. 137, 22A528 (2012)

    Article  Google Scholar 

  57. J.E. Subotnik, N. Shenvi, J. Chem. Phys. 134, 024105 (2011)

    Article  ADS  Google Scholar 

  58. J.E. Subotnik, N. Shenvi, J. Chem. Phys. 134, 244114 (2011)

    Article  ADS  Google Scholar 

  59. I. Tavernelli, Phys. Rev. B 73, 094204 (2006)

    Article  ADS  Google Scholar 

  60. J.L. Alonso, J. Clemente-Gallardo, P. Echeniche-Robba, J.A. Jover-Galtier, J. Chem. Phys. 139, 087101 (2013)

    Article  ADS  Google Scholar 

  61. A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 139, 087102 (2013)

    Article  ADS  Google Scholar 

  62. F. Agostini, S.K. Min, E.K.U. Gross, Ann. Phys. 527, 546 (2015)

    Article  MathSciNet  Google Scholar 

  63. F.G. Eich, F. Agostini, J. Chem. Phys. 145, 054110 (2016)

    Article  ADS  Google Scholar 

  64. B.F.E. Curchod, F. Agostini, E.K.U. Gross, J. Chem. Phys. 145, 034103 (2016)

    Article  ADS  Google Scholar 

  65. B.F.E. Curchod, F. Agostini, J. Phys. Chem. Lett. 8, 831 (2017)

    Article  Google Scholar 

  66. E. Khosravi, A. Abedi, A. Rubio, N.T. Maitra, Phys. Chem. Chem. Phys. 19, 8269 (2017)

    Article  Google Scholar 

  67. Y. Suzuki, K. Watanabe, Phys. Rev. A 94, 032517 (2016)

    Article  ADS  Google Scholar 

  68. Y. Suzuki, A. Abedi, N.T. Maitra, K. Yamashita, E.K.U. Gross, Phys. Rev. A 89, 040501(R) (2014)

    Article  ADS  Google Scholar 

  69. E. Khosravi, A. Abedi, N.T. Maitra, Phys. Rev. Lett. 115, 263002 (2015)

    Article  ADS  Google Scholar 

  70. S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, Phys. Rev. Lett. 113, 263004 (2014)

    Article  ADS  Google Scholar 

  71. R. Requist, F. Tandetzky, E.K.U. Gross, Phys. Rev. A 93, 042108 (2016)

    Article  ADS  Google Scholar 

  72. P.R. Holland, The quantum theory of motion – an account of the de Broglie–Bohm causal interpretation of quantum mechanics (Cambridge University Press, Cambridge, UK, 1993)

  73. B.F.E. Curchod, T.J. Martínez, Chem. Rev. 118, 3305 (2018)

    Article  Google Scholar 

  74. E.J. Heller, J. Chem. Phys. 75, 2923 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  75. S. Yang, J.D. Coe, B. Kaduk, T.J. Martínez, J. Chem. Phys. 130, 04B606 (2009)

    Google Scholar 

  76. B. Mignolet, B.F.E. Curchod, arXiv:1801.06639 (2018)

  77. B.G. Levine, J.D. Coe, A.M. Virshup, T.J. Martinez, Chem. Phys. 347, 3 (2008)

    Article  ADS  Google Scholar 

  78. J.W. Snyder Jr., B.F.E. Curchod, T.J. Martínez, J. Phys. Chem. Lett. 7, 2444 (2016)

    Article  Google Scholar 

  79. H. Tao, B.G. Levine, T.J. Martínez, J. Chem. Phys. A 113, 13656 (2009)

    Article  Google Scholar 

  80. S. Pijeau, D. Foster, E.G. Hohenstein, J. Phys. Chem. A 121, 4595 (2017)

    Article  Google Scholar 

  81. B.F.E. Curchod, A. Sisto, T.J. Martínez, J. Phys. Chem. A 121, 265 (2017)

    Article  Google Scholar 

  82. CPMD, Copyright IBM Corp 1990–2015, Copyright MPI für Festkörperforschung Stuttgart 1997–2001. http://www.cpmd.org/

  83. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    Article  ADS  Google Scholar 

  84. E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)

    Article  ADS  Google Scholar 

  85. M. Petersilka, U.J. Gossmann, E.K.U. Gross, Phys. Rev. Lett. 76, 1212 (1996)

    Article  ADS  Google Scholar 

  86. M.E. Casida, Time-dependent density-functional response theory for molecules, in Recent advances in density functional methods, edited by D.P. Chong (World Scientific, Singapore, 1995), p. 155

  87. I. Tamm, J. Phys. 9, 449 (1945)

    Google Scholar 

  88. S.M. Dancoff, Phys. Rev. 78, 382 (1950)

    Article  ADS  Google Scholar 

  89. C.A. Ullrich, Time-dependent density-functional theory (Oxford University Press, 2012)

  90. B.G. Levine, C. Ko, J. Quenneville, T.J. Martinez, Mol. Phys. 104, 1039 (2006)

    Article  ADS  Google Scholar 

  91. E. Tapavicza, I. Tavernelli, U. Rothlisberger, C. Filippi, M.E. Casida, J. Chem. Phys. 129, 124108 (2008)

    Article  ADS  Google Scholar 

  92. L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48, 1425 (1982)

    Article  ADS  Google Scholar 

  93. C.M. Isborn, N. Luehr, I.S. Ufimtsev, T.J. Martínez, J. Chem. Theory Comput. 7, 1814 (2011)

    Article  Google Scholar 

  94. I.S. Ufimtsev, T.J. Martinez, J. Chem. Theory Comput. 4, 222 (2008)

    Article  Google Scholar 

  95. I.S. Ufimtsev, T.J. Martinez, J. Chem. Theory Comput. 5, 1004 (2009)

    Article  Google Scholar 

  96. I.S. Ufimtsev, T.J. Martinez, J. Chem. Theory Comput. 5, 2619 (2009)

    Article  Google Scholar 

  97. R. Ditchfield, W.J. Hehre, J.A. Pople, J. Chem. Phys. 54, 724 (1971)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, Durham University, South Road, Durham, DH1 3LE, UK

    Basile F. E. Curchod

  2. Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, 91405, Orsay, France

    Federica Agostini

  3. IBM Research GmbH, Zürich Research Laboratory, 8803, Rüschlikon, Switzerland

    Ivano Tavernelli

Authors
  1. Basile F. E. Curchod
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  2. Federica Agostini
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  3. Ivano Tavernelli
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Correspondence to Ivano Tavernelli.

Additional information

Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.

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Curchod, B.F.E., Agostini, F. & Tavernelli, I. CT-MQC – a coupled-trajectory mixed quantum/classical method including nonadiabatic quantum coherence effects. Eur. Phys. J. B 91, 168 (2018). https://doi.org/10.1140/epjb/e2018-90149-x

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